Legal claims defining the scope of protection. Each claim is shown in both the original legal language and a plain English translation.
1. A method for propagating the state of an object and an uncertainty associated with the state of the object, the method comprising: receiving, by a computer system, an interval of time over which the uncertainty is to be propagated, as well as an ensemble of initial conditions that characterize the initial uncertainty associated with the state of an object and an ordinary differential equation (ODE) describing dynamics of the state of the object, which together define an initial value problem (IVP) ensemble, for the object, the IVP ensemble comprising a plurality of IVPs; solving, by the computer system, the IVPs in the IVP ensemble wherein the solution of one or more of the IVPs in the IVP ensemble depends upon the solution of one or more of the other IVPs in the IVP ensemble; characterizing, by the computer system, the uncertainty associated with the state of the object at the end of the time interval based on solving the IVPs in the IVP ensemble.
A computer system calculates the uncertainty of an object's future state. It receives a time interval, a set of possible initial states (an "ensemble" representing initial uncertainty), and an equation describing the object's motion (an ordinary differential equation or ODE). These define multiple "initial value problems" (IVPs). The system solves these IVPs, where solving some IVPs depends on the solutions of others. Finally, it determines the object's uncertainty at the end of the time interval based on these IVP solutions.
2. The method of claim 1 , wherein the solution of one or more of the IVPs, over one or more time steps, is used within the process of solving one or more of the remaining IVPs, over one or more time steps.
Building upon the method of calculating the uncertainty of an object's future state by receiving a time interval, a set of possible initial states (an "ensemble" representing initial uncertainty), and an equation describing the object's motion (an ordinary differential equation or ODE) that define multiple "initial value problems" (IVPs) that are solved by the system to determine the object's uncertainty at the end of the time interval, this claim specifies that the solution of some IVPs at certain time steps is used while solving other IVPs at similar time steps. This reuse of intermediate solutions improves computational efficiency.
3. The method of claim 1 , wherein one or more time steps taken to solve one or more of the IVPs in the IVP ensemble are the same as one or more time steps taken to solve one or more of the remaining IVPs in the IVP ensemble.
Building upon the method of calculating the uncertainty of an object's future state by receiving a time interval, a set of possible initial states (an "ensemble" representing initial uncertainty), and an equation describing the object's motion (an ordinary differential equation or ODE) that define multiple "initial value problems" (IVPs) that are solved by the system to determine the object's uncertainty at the end of the time interval, this claim specifies that when solving the IVPs, the same time steps are used for different IVPs within the ensemble. This synchronization of time steps enables sharing and reuse of intermediate calculations.
4. The method of claim 1 , wherein the solution of one or more of the IVPs, over one or more time steps, is used within the process of solving one or more of the remaining IVPs, over one or more time steps, and wherein one or more the time steps taken to solve one or more of the IVPs in the IVP ensemble are the same as one or more time steps taken to solve one or more of the remaining IVPs in the IVP ensemble.
Building upon the method of calculating the uncertainty of an object's future state by receiving a time interval, a set of possible initial states (an "ensemble" representing initial uncertainty), and an equation describing the object's motion (an ordinary differential equation or ODE) that define multiple "initial value problems" (IVPs) that are solved by the system to determine the object's uncertainty at the end of the time interval, this claim combines the previous two optimizations: the solution of some IVPs at certain time steps is used while solving other IVPs at similar time steps, and the same time steps are used for different IVPs within the ensemble.
5. The method of claim 1 , wherein one or more of the numerical methods used to solve one or more of the IVPs in the IVP ensemble is an implicit Runge-Kutta method.
Building upon the method of calculating the uncertainty of an object's future state by receiving a time interval, a set of possible initial states (an "ensemble" representing initial uncertainty), and an equation describing the object's motion (an ordinary differential equation or ODE) that define multiple "initial value problems" (IVPs) that are solved by the system to determine the object's uncertainty at the end of the time interval, this claim specifies that an "implicit Runge-Kutta method" is used as a numerical method to solve the IVPs. This numerical method choice is important for the efficient and stable solution of the differential equations.
6. The method of claim 2 , wherein one or more of the numerical methods used to solve one or more of the IVPs in the IVP ensemble is an implicit Runge-Kutta method.
Building upon the method of calculating the uncertainty of an object's future state by receiving a time interval, a set of possible initial states (an "ensemble" representing initial uncertainty), and an equation describing the object's motion (an ordinary differential equation or ODE) that define multiple "initial value problems" (IVPs) that are solved by the system to determine the object's uncertainty at the end of the time interval, and the specification that the solution of some IVPs at certain time steps is used while solving other IVPs at similar time steps, this claim specifies that an "implicit Runge-Kutta method" is used as a numerical method to solve the IVPs. This numerical method choice is important for the efficient and stable solution of the differential equations.
7. The method of claim 3 , wherein one or more of the numerical methods used to solve one or more of the IVPs in the IVP ensemble is an implicit Runge-Kutta method.
Building upon the method of calculating the uncertainty of an object's future state by receiving a time interval, a set of possible initial states (an "ensemble" representing initial uncertainty), and an equation describing the object's motion (an ordinary differential equation or ODE) that define multiple "initial value problems" (IVPs) that are solved by the system to determine the object's uncertainty at the end of the time interval, and the specification that the same time steps are used for different IVPs within the ensemble, this claim specifies that an "implicit Runge-Kutta method" is used as a numerical method to solve the IVPs. This numerical method choice is important for the efficient and stable solution of the differential equations.
8. The method of claim 4 , wherein one or more of the numerical methods used to solve one or more of the IVPs in the IVP ensemble is an implicit Runge-Kutta method.
Building upon the method of calculating the uncertainty of an object's future state by receiving a time interval, a set of possible initial states (an "ensemble" representing initial uncertainty), and an equation describing the object's motion (an ordinary differential equation or ODE) that define multiple "initial value problems" (IVPs) that are solved by the system to determine the object's uncertainty at the end of the time interval, and the specification that the solution of some IVPs at certain time steps is used while solving other IVPs at similar time steps, along with the specification that the same time steps are used for different IVPs within the ensemble, this claim specifies that an "implicit Runge-Kutta method" is used as a numerical method to solve the IVPs. This numerical method choice is important for the efficient and stable solution of the differential equations.
9. The method of claim 5 , wherein one or more of the implicit Runge-Kutta methods is estimating and controlling the truncation error.
Building upon the method of calculating the uncertainty of an object's future state by receiving a time interval, a set of possible initial states (an "ensemble" representing initial uncertainty), and an equation describing the object's motion (an ordinary differential equation or ODE) that define multiple "initial value problems" (IVPs) that are solved by the system to determine the object's uncertainty at the end of the time interval, and the specification that an "implicit Runge-Kutta method" is used as a numerical method to solve the IVPs, this claim further refines the method by estimating and controlling the truncation error associated with the implicit Runge-Kutta method. This ensures accuracy by limiting the error introduced by the numerical approximation.
10. The method of claim 6 , wherein one or more of the implicit Runge-Kutta methods is estimating and controlling the truncation error.
Building upon the method of calculating the uncertainty of an object's future state by receiving a time interval, a set of possible initial states (an "ensemble" representing initial uncertainty), and an equation describing the object's motion (an ordinary differential equation or ODE) that define multiple "initial value problems" (IVPs) that are solved by the system to determine the object's uncertainty at the end of the time interval, and the specification that the solution of some IVPs at certain time steps is used while solving other IVPs at similar time steps, along with the specification that an "implicit Runge-Kutta method" is used as a numerical method to solve the IVPs, this claim further refines the method by estimating and controlling the truncation error associated with the implicit Runge-Kutta method. This ensures accuracy by limiting the error introduced by the numerical approximation.
11. The method of claim 7 , wherein one or more of the implicit Runge-Kutta methods is estimating and controlling the truncation error.
Building upon the method of calculating the uncertainty of an object's future state by receiving a time interval, a set of possible initial states (an "ensemble" representing initial uncertainty), and an equation describing the object's motion (an ordinary differential equation or ODE) that define multiple "initial value problems" (IVPs) that are solved by the system to determine the object's uncertainty at the end of the time interval, and the specification that the same time steps are used for different IVPs within the ensemble, along with the specification that an "implicit Runge-Kutta method" is used as a numerical method to solve the IVPs, this claim further refines the method by estimating and controlling the truncation error associated with the implicit Runge-Kutta method. This ensures accuracy by limiting the error introduced by the numerical approximation.
12. The method of claim 8 , wherein one or more of the implicit Runge-Kutta methods is estimating and controlling the truncation error.
Building upon the method of calculating the uncertainty of an object's future state by receiving a time interval, a set of possible initial states (an "ensemble" representing initial uncertainty), and an equation describing the object's motion (an ordinary differential equation or ODE) that define multiple "initial value problems" (IVPs) that are solved by the system to determine the object's uncertainty at the end of the time interval, and the specification that the solution of some IVPs at certain time steps is used while solving other IVPs at similar time steps, along with the specification that the same time steps are used for different IVPs within the ensemble, and also the specification that an "implicit Runge-Kutta method" is used as a numerical method to solve the IVPs, this claim further refines the method by estimating and controlling the truncation error associated with the implicit Runge-Kutta method. This ensures accuracy by limiting the error introduced by the numerical approximation.
13. A system comprising: a processor; and a memory coupled with the processor and having stored therein a sequence of instructions which, when executed by the processor, cause the processor to propagate the state of an object and an uncertainty associated with the state of the object by: receiving an interval of time over which the uncertainty is to be propagated, as well as an ensemble of initial conditions that characterize the initial uncertainty associated with the state of an object and an ordinary differential equation (ODE) describing dynamics of the state of the object, which together define an initial value problem (IVP) ensemble, for the object, the IVP ensemble comprising a plurality of IVPs; solving one or more of the IVPs in the IVP ensemble wherein the solution of one or more of the IVPs in the IVP ensemble depends upon the solution of one or more of the other IVPs in the IVP ensemble; and characterizing the uncertainty associated with the state of the object at the end of the time interval based on solving the IVPs in the IVP ensemble.
A computer system calculates the uncertainty of an object's future state. It includes a processor and memory with instructions to: receive a time interval, a set of possible initial states (an "ensemble" representing initial uncertainty), and an equation describing the object's motion (an ordinary differential equation or ODE). These define multiple "initial value problems" (IVPs). The system solves these IVPs, where solving some IVPs depends on the solutions of others. Finally, it determines the object's uncertainty at the end of the time interval based on these IVP solutions.
14. The system of claim 13 , wherein the solution of one or more of the IVPs, over one or more time steps, is used within the process of solving one or more of the remaining IVPs, over one or more time steps.
Building upon the system that calculates the uncertainty of an object's future state by receiving a time interval, a set of possible initial states (an "ensemble" representing initial uncertainty), and an equation describing the object's motion (an ordinary differential equation or ODE) that define multiple "initial value problems" (IVPs) that are solved by the system to determine the object's uncertainty at the end of the time interval, this claim specifies that the solution of some IVPs at certain time steps is used while solving other IVPs at similar time steps. This reuse of intermediate solutions improves computational efficiency.
15. The system of claim 13 , wherein one or more time steps taken to solve one or more of the IVPs in the IVP ensemble are the same as one or more time steps taken to solve one or more of the remaining IVPs in the IVP ensemble.
Building upon the system that calculates the uncertainty of an object's future state by receiving a time interval, a set of possible initial states (an "ensemble" representing initial uncertainty), and an equation describing the object's motion (an ordinary differential equation or ODE) that define multiple "initial value problems" (IVPs) that are solved by the system to determine the object's uncertainty at the end of the time interval, this claim specifies that when solving the IVPs, the same time steps are used for different IVPs within the ensemble. This synchronization of time steps enables sharing and reuse of intermediate calculations.
16. The system of claim 13 , wherein the solution of one or more of the IVPs, over one or more time steps, is used within the process of solving one or more of the remaining IVPs, over one or more time steps, and wherein one or more time steps taken to solve one or more of the IVPs in the IVP ensemble are the same as one or more time steps taken to solve one or more of the remaining IVPs in the IVP ensemble.
Building upon the system that calculates the uncertainty of an object's future state by receiving a time interval, a set of possible initial states (an "ensemble" representing initial uncertainty), and an equation describing the object's motion (an ordinary differential equation or ODE) that define multiple "initial value problems" (IVPs) that are solved by the system to determine the object's uncertainty at the end of the time interval, this claim combines the previous two optimizations: the solution of some IVPs at certain time steps is used while solving other IVPs at similar time steps, and the same time steps are used for different IVPs within the ensemble.
17. The system of claim 13 , wherein one or more of the numerical methods used to solve one or more of the IVPs in the IVP ensemble is an implicit Runge-Kutta method.
Building upon the system that calculates the uncertainty of an object's future state by receiving a time interval, a set of possible initial states (an "ensemble" representing initial uncertainty), and an equation describing the object's motion (an ordinary differential equation or ODE) that define multiple "initial value problems" (IVPs) that are solved by the system to determine the object's uncertainty at the end of the time interval, this claim specifies that an "implicit Runge-Kutta method" is used as a numerical method to solve the IVPs. This numerical method choice is important for the efficient and stable solution of the differential equations.
18. The system of claim 14 , wherein one or more of the numerical methods used to solve one or more of the IVPs in the IVP ensemble is an implicit Runge-Kutta method.
This system is designed to compute and track an object's state and its associated uncertainty over time. It starts by receiving three key inputs: a specific time interval for the calculation, a collection of initial conditions representing the object's initial uncertainty, and an ordinary differential equation (ODE) that describes how the object's state changes. These inputs together form a group of interconnected Initial Value Problems (IVPs). The system then proceeds to solve these IVPs. A defining characteristic of this process is that the intermediate solution of one or more IVPs, taken over one or more time steps, is utilized or fed into the process of solving other remaining IVPs in the ensemble during those same or different time steps. For at least one of these IVPs, the system employs an implicit Runge-Kutta method as its numerical solver. Finally, based on the completed solutions of all the IVPs, the system determines and characterizes the object's uncertainty at the end of the specified time interval. ERROR (embedding): Error: Failed to save embedding: Could not find the 'embedding' column of 'patent_claims' in the schema cache
19. The system of claim 15 , wherein one or more of the numerical methods used to solve one or more of the IVPs in the IVP ensemble is an implicit Runge-Kutta method.
Building upon the system that calculates the uncertainty of an object's future state by receiving a time interval, a set of possible initial states (an "ensemble" representing initial uncertainty), and an equation describing the object's motion (an ordinary differential equation or ODE) that define multiple "initial value problems" (IVPs) that are solved by the system to determine the object's uncertainty at the end of the time interval, and the specification that the same time steps are used for different IVPs within the ensemble, this claim specifies that an "implicit Runge-Kutta method" is used as a numerical method to solve the IVPs. This numerical method choice is important for the efficient and stable solution of the differential equations.
20. The system of claim 16 , wherein one or more of the numerical methods used to solve one or more of the IVPs in the IVP ensemble is an implicit Runge-Kutta method.
Building upon the system that calculates the uncertainty of an object's future state by receiving a time interval, a set of possible initial states (an "ensemble" representing initial uncertainty), and an equation describing the object's motion (an ordinary differential equation or ODE) that define multiple "initial value problems" (IVPs) that are solved by the system to determine the object's uncertainty at the end of the time interval, and the specification that the solution of some IVPs at certain time steps is used while solving other IVPs at similar time steps, along with the specification that the same time steps are used for different IVPs within the ensemble, this claim specifies that an "implicit Runge-Kutta method" is used as a numerical method to solve the IVPs. This numerical method choice is important for the efficient and stable solution of the differential equations.
21. The system of claim 17 , wherein one or more of the implicit Runge-Kutta methods is estimating and controlling the truncation error.
Building upon the system that calculates the uncertainty of an object's future state by receiving a time interval, a set of possible initial states (an "ensemble" representing initial uncertainty), and an equation describing the object's motion (an ordinary differential equation or ODE) that define multiple "initial value problems" (IVPs) that are solved by the system to determine the object's uncertainty at the end of the time interval, and the specification that an "implicit Runge-Kutta method" is used as a numerical method to solve the IVPs, this claim further refines the system by estimating and controlling the truncation error associated with the implicit Runge-Kutta method. This ensures accuracy by limiting the error introduced by the numerical approximation.
22. The system of claim 18 , wherein one or more of the implicit Runge-Kutta methods is estimating and controlling the truncation error.
Building upon the system that calculates the uncertainty of an object's future state by receiving a time interval, a set of possible initial states (an "ensemble" representing initial uncertainty), and an equation describing the object's motion (an ordinary differential equation or ODE) that define multiple "initial value problems" (IVPs) that are solved by the system to determine the object's uncertainty at the end of the time interval, and the specification that the solution of some IVPs at certain time steps is used while solving other IVPs at similar time steps, along with the specification that an "implicit Runge-Kutta method" is used as a numerical method to solve the IVPs, this claim further refines the system by estimating and controlling the truncation error associated with the implicit Runge-Kutta method. This ensures accuracy by limiting the error introduced by the numerical approximation.
23. The system of claim 19 , wherein one or more of the implicit Runge-Kutta methods is estimating and controlling the truncation error.
Building upon the system that calculates the uncertainty of an object's future state by receiving a time interval, a set of possible initial states (an "ensemble" representing initial uncertainty), and an equation describing the object's motion (an ordinary differential equation or ODE) that define multiple "initial value problems" (IVPs) that are solved by the system to determine the object's uncertainty at the end of the time interval, and the specification that the same time steps are used for different IVPs within the ensemble, along with the specification that an "implicit Runge-Kutta method" is used as a numerical method to solve the IVPs, this claim further refines the system by estimating and controlling the truncation error associated with the implicit Runge-Kutta method. This ensures accuracy by limiting the error introduced by the numerical approximation.
24. The system of claim 20 , wherein one or more of the implicit Runge-Kutta methods is estimating and controlling the truncation error.
Building upon the system that calculates the uncertainty of an object's future state by receiving a time interval, a set of possible initial states (an "ensemble" representing initial uncertainty), and an equation describing the object's motion (an ordinary differential equation or ODE) that define multiple "initial value problems" (IVPs) that are solved by the system to determine the object's uncertainty at the end of the time interval, and the specification that the solution of some IVPs at certain time steps is used while solving other IVPs at similar time steps, along with the specification that the same time steps are used for different IVPs within the ensemble, and also the specification that an "implicit Runge-Kutta method" is used as a numerical method to solve the IVPs, this claim further refines the system by estimating and controlling the truncation error associated with the implicit Runge-Kutta method. This ensures accuracy by limiting the error introduced by the numerical approximation.
25. A computer-readable memory having stored therein a sequence of instructions which, when executed by a processor, cause the processor to propagate the state of an object and an uncertainty associated with the state of the object by: receiving an interval of time over which the uncertainty is to be propagated, as well as an ensemble of initial conditions that characterize the initial uncertainty associated with the state of an object and an ordinary differential equation (ODE) describing dynamics of the state of the object, which together define an initial value problem (IVP) ensemble, for the object, the IVP ensemble comprising a plurality of IVPs; solving one or more of the IVPs in the IVP ensemble wherein the solution of one or more of the IVPs in the IVP ensemble depends upon the solution of one or more of the other IVPs in the IVP ensemble; and characterizing the uncertainty associated with the state of the object at the end of the time interval based on solving the IVPs in the IVP ensemble.
A computer-readable memory stores instructions for calculating the uncertainty of an object's future state. When executed, the instructions cause a processor to: receive a time interval, a set of possible initial states (an "ensemble" representing initial uncertainty), and an equation describing the object's motion (an ordinary differential equation or ODE). These define multiple "initial value problems" (IVPs). The system solves these IVPs, where solving some IVPs depends on the solutions of others. Finally, it determines the object's uncertainty at the end of the time interval based on these IVP solutions.
26. The computer-readable memory of claim 25 , wherein the solution of one or more of the IVPs, over one or more time steps, is used within the process of solving one or more of the remaining IVPs, over one or more time steps.
Building upon the computer-readable memory that stores instructions for calculating the uncertainty of an object's future state by receiving a time interval, a set of possible initial states (an "ensemble" representing initial uncertainty), and an equation describing the object's motion (an ordinary differential equation or ODE) that define multiple "initial value problems" (IVPs) that are solved by the system to determine the object's uncertainty at the end of the time interval, this claim specifies that the solution of some IVPs at certain time steps is used while solving other IVPs at similar time steps. This reuse of intermediate solutions improves computational efficiency.
27. The computer-readable memory of claim 25 , wherein one or more time steps taken to solve one or more of the IVPs in the IVP ensemble are the same as one or more time steps taken to solve one or more of the remaining IVPs in the IVP ensemble.
Building upon the computer-readable memory that stores instructions for calculating the uncertainty of an object's future state by receiving a time interval, a set of possible initial states (an "ensemble" representing initial uncertainty), and an equation describing the object's motion (an ordinary differential equation or ODE) that define multiple "initial value problems" (IVPs) that are solved by the system to determine the object's uncertainty at the end of the time interval, this claim specifies that when solving the IVPs, the same time steps are used for different IVPs within the ensemble. This synchronization of time steps enables sharing and reuse of intermediate calculations.
28. The computer-readable memory of claim 25 , wherein the solution of one or more of the IVPs, over one or more time steps, is used within the process of solving one or more of the remaining IVPs, over one or more time steps, and wherein one or more time steps taken to solve one or more of the IVPs in the IVP ensemble are the same as one or more time steps taken to solve one or more of the remaining IVPs in the IVP ensemble.
Building upon the computer-readable memory that stores instructions for calculating the uncertainty of an object's future state by receiving a time interval, a set of possible initial states (an "ensemble" representing initial uncertainty), and an equation describing the object's motion (an ordinary differential equation or ODE) that define multiple "initial value problems" (IVPs) that are solved by the system to determine the object's uncertainty at the end of the time interval, this claim combines the previous two optimizations: the solution of some IVPs at certain time steps is used while solving other IVPs at similar time steps, and the same time steps are used for different IVPs within the ensemble.
29. The computer-readable memory of claim 25 , wherein one or more of the numerical methods used to solve one or more of the IVPs in the IVP ensemble is an implicit Runge-Kutta method.
Building upon the computer-readable memory that stores instructions for calculating the uncertainty of an object's future state by receiving a time interval, a set of possible initial states (an "ensemble" representing initial uncertainty), and an equation describing the object's motion (an ordinary differential equation or ODE) that define multiple "initial value problems" (IVPs) that are solved by the system to determine the object's uncertainty at the end of the time interval, this claim specifies that an "implicit Runge-Kutta method" is used as a numerical method to solve the IVPs. This numerical method choice is important for the efficient and stable solution of the differential equations.
30. The computer-readable memory of claim 26 , wherein one or more of the numerical methods used to solve one or more of the IVPs in the IVP ensemble is an implicit Runge-Kutta method.
Building upon the computer-readable memory that stores instructions for calculating the uncertainty of an object's future state by receiving a time interval, a set of possible initial states (an "ensemble" representing initial uncertainty), and an equation describing the object's motion (an ordinary differential equation or ODE) that define multiple "initial value problems" (IVPs) that are solved by the system to determine the object's uncertainty at the end of the time interval, and the specification that the solution of some IVPs at certain time steps is used while solving other IVPs at similar time steps, this claim specifies that an "implicit Runge-Kutta method" is used as a numerical method to solve the IVPs. This numerical method choice is important for the efficient and stable solution of the differential equations.
31. The computer-readable memory of claim 27 , wherein one or more of the numerical methods used to solve one or more of the IVPs in the IVP ensemble is an implicit Runge-Kutta method.
Building upon the computer-readable memory that stores instructions for calculating the uncertainty of an object's future state by receiving a time interval, a set of possible initial states (an "ensemble" representing initial uncertainty), and an equation describing the object's motion (an ordinary differential equation or ODE) that define multiple "initial value problems" (IVPs) that are solved by the system to determine the object's uncertainty at the end of the time interval, and the specification that the same time steps are used for different IVPs within the ensemble, this claim specifies that an "implicit Runge-Kutta method" is used as a numerical method to solve the IVPs. This numerical method choice is important for the efficient and stable solution of the differential equations.
32. The computer-readable memory of claim 28 , wherein one or more of the numerical methods used to solve one or more of the IVPs in the IVP ensemble is an implicit Runge-Kutta method.
Building upon the computer-readable memory that stores instructions for calculating the uncertainty of an object's future state by receiving a time interval, a set of possible initial states (an "ensemble" representing initial uncertainty), and an equation describing the object's motion (an ordinary differential equation or ODE) that define multiple "initial value problems" (IVPs) that are solved by the system to determine the object's uncertainty at the end of the time interval, and the specification that the solution of some IVPs at certain time steps is used while solving other IVPs at similar time steps, along with the specification that the same time steps are used for different IVPs within the ensemble, this claim specifies that an "implicit Runge-Kutta method" is used as a numerical method to solve the IVPs. This numerical method choice is important for the efficient and stable solution of the differential equations.
33. The computer-readable memory of claim 29 , wherein one or more of the implicit Runge-Kutta methods is estimating and controlling the truncation error.
Building upon the computer-readable memory that stores instructions for calculating the uncertainty of an object's future state by receiving a time interval, a set of possible initial states (an "ensemble" representing initial uncertainty), and an equation describing the object's motion (an ordinary differential equation or ODE) that define multiple "initial value problems" (IVPs) that are solved by the system to determine the object's uncertainty at the end of the time interval, and the specification that an "implicit Runge-Kutta method" is used as a numerical method to solve the IVPs, this claim further refines the stored instructions to estimate and control the truncation error associated with the implicit Runge-Kutta method. This ensures accuracy by limiting the error introduced by the numerical approximation.
34. The computer-readable memory of claim 30 , wherein one or more of the implicit Runge-Kutta methods is estimating and controlling the truncation error.
Building upon the computer-readable memory that stores instructions for calculating the uncertainty of an object's future state by receiving a time interval, a set of possible initial states (an "ensemble" representing initial uncertainty), and an equation describing the object's motion (an ordinary differential equation or ODE) that define multiple "initial value problems" (IVPs) that are solved by the system to determine the object's uncertainty at the end of the time interval, and the specification that the solution of some IVPs at certain time steps is used while solving other IVPs at similar time steps, along with the specification that an "implicit Runge-Kutta method" is used as a numerical method to solve the IVPs, this claim further refines the stored instructions to estimate and control the truncation error associated with the implicit Runge-Kutta method. This ensures accuracy by limiting the error introduced by the numerical approximation.
35. The computer-readable memory of claim 31 , wherein one or more of the implicit Runge-Kutta methods is estimating and controlling the truncation error.
Building upon the computer-readable memory that stores instructions for calculating the uncertainty of an object's future state by receiving a time interval, a set of possible initial states (an "ensemble" representing initial uncertainty), and an equation describing the object's motion (an ordinary differential equation or ODE) that define multiple "initial value problems" (IVPs) that are solved by the system to determine the object's uncertainty at the end of the time interval, and the specification that the same time steps are used for different IVPs within the ensemble, along with the specification that an "implicit Runge-Kutta method" is used as a numerical method to solve the IVPs, this claim further refines the stored instructions to estimate and control the truncation error associated with the implicit Runge-Kutta method. This ensures accuracy by limiting the error introduced by the numerical approximation.
36. The computer-readable memory of claim 32 , wherein one or more of the implicit Runge-Kutta methods is estimating and controlling the truncation error.
Building upon the computer-readable memory that stores instructions for calculating the uncertainty of an object's future state by receiving a time interval, a set of possible initial states (an "ensemble" representing initial uncertainty), and an equation describing the object's motion (an ordinary differential equation or ODE) that define multiple "initial value problems" (IVPs) that are solved by the system to determine the object's uncertainty at the end of the time interval, and the specification that the solution of some IVPs at certain time steps is used while solving other IVPs at similar time steps, along with the specification that the same time steps are used for different IVPs within the ensemble, and also the specification that an "implicit Runge-Kutta method" is used as a numerical method to solve the IVPs, this claim further refines the stored instructions to estimate and control the truncation error associated with the implicit Runge-Kutta method. This ensures accuracy by limiting the error introduced by the numerical approximation.
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December 9, 2014
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